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Despite the need for reliable statistical information, there is no systematic monitoring of scientific migration flows in Russia. The Federal State Statistics Service, the specialized portals of the Ministry of Education and Science of Russia, and a number of research projects make it possible to compose a «mosaic» of various kinds of assessments, including the number of foreign scientific staff working in Russia and the number of domestic researchers sent to foreign internships. This article reviews these estimates and shows that they are very incomplete and often contradictory. Therefore, it is not possible to estimate accurately the extent of this migration; we can only give an approximate estimate and identify its characteristic trends.